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Coupling between scattering channels with SUSY transformations for equal thresholds

par Pupasov, Andrey ;Samsonov, Boris ;Sparenberg, Jean-Marc ;Baye, Daniel Jean
Référence Journal of Physics A: Mathematical and Theoretical, 42, page (195303)
Publication Publié, 2009-04-27

Article révisé par les pairs

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Résumé :

Supersymmetric (SUSY) transformations of the multichannel Schrödinger equation with equal thresholds and arbitrary partial waves in all channels are studied. The structures of the transformation function and the superpotential are analysed. Relations between Jost and scattering matrices of superpartner potentials are obtained. In particular, we show that a special type of SUSY transformation allows us to introduce a coupling between scattering channels starting from a potential with an uncoupled scattering matrix. The possibility for this coupling to be trivial is discussed. We show that the transformation introduces bound and virtual states with a definite degeneracy at the factorization energy. A detailed study of the potential and scattering matrices is given for the 2 × 2 case. The possibility of inverting coupled- channel scattering data by such a SUSY transformation is demonstrated by several examples (s–s, s–p and s–d partial waves).